Regular grease is for lubricating wear surfaces you can directly access and that you want to reduce friction of. For example threads, bearings etc. I use boat trailer grease because it is cheap and water doesn't displace it well. Don't sweat the specific brand, we talk about bicycles and not high temperature and high rpm applications like automotive or aviation etc. Use a light-colored grease so you can see if it got dirty.
Oil is used where you can't access the wearing surface and the oil needs to wick to the are requiring lubrication. Examples include the chain.
Surfaces that require MORE friction use an assembly grease. It basically is a regular grease (for corrosion protection) that has grit included to INCREASE friction. Sometimes this paste is called assembly or carbon paste. Seatposts and stems are examples of use. Never ever mix up assembly and regular grease.